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A continuous model of optimal-cost routes in a circular city

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Abstract

This paper deals with the determination of optimal-cost routes in a circular city where the routes are not confined to a discrete network, but may vary continuously. The Euler-Lagrange equation is derived for the general radially-symmetric case for position-dependent cost. This equation is solved by quadratures. In a special case, the integral representation is evaluated explicitly. A model of a circular city is then assumed, consisting of a circular central business district surrounded by a transition zone. A detailed analysis is then carried out which permits the determination of optimal-cost routes. The results may be employed to improve decision-making in regard to whether to build bypasses around, or direct routes through, a city.

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Authors and Affiliations

  1. Purdue University, Lafayette, Indiana

    N. R. Zitron (Associate Professor of Mathematics)

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  1. N. R. Zitron
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Communicated by G. Leitmann

This research was carried out while the author was on sabbatical leave at the Department of Mathematics, Stanford University, Stanford, California. The author would like to express his thanks to Professor M. M. Schiffer of the Mathematics Department, Stanford University, for some stimulating discussions and to Professor G. F. Newell of the Division of Transportation Engineering, Department of Civil Engineering, University of California at Berkeley, for the use of his department's facilities.

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Zitron, N.R. A continuous model of optimal-cost routes in a circular city. J Optim Theory Appl 14, 291–303 (1974). https://doi.org/10.1007/BF00932612

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